Image Partitioning Into Convex Polygons Based On Voronoi Diagrams

The segmentation of images into atomic regions is a very important technique for studying and analyzing images in the field of computer vision.Traditional superpixel seg?mentation algorithms usually perform at the pixel level which causes the problem that they can't directly capture the geometric information disseminated into the images.This paper proposes an image segmentation algorithm by operating at the level of geometric shapes.The algorithm partitions image into a few convex polygons.The image regions composed of these convex polygons are compact and they can reflect the geometric information in the image well.Furthermore,region convexity insures a unique adjacency graph between re-gions,without ambiguities.Voronoi diagram,also known as Voronoi tessellation,is a very important concept in Geometry.It is widely used in GIS,life science,computer graphics and image processing.Our algorithm partitions images based on Voronoi diagrams.The Voronoi cells are guaranteed to be convex polygons without overlap and empty space.Our objective function has two terms.The first term of the objective function is called the image approximation term which is used to ensure that the segmentation boundary can be consistent with the image boundary.The other one is called graphic regularity term which ensures the size and shape of each segmented convex polygon remain uniform.All convex polygons are compact.We use the gradient of the objective function to optimize the objective function.We do not use the traditional gradient descent method because the function is not continuous and its anisotropy leads to the unstable derivative.So we improve the traditional gradient descent method to optimize the objective function.The segmentation algorithm is more suitable for images with strong geometric features.The segmentation results of this algorithm are more excellent especially for the images containing man-made objects.In this thesis,a large number of experiments are performed and the influences of the changes of related parameters on the segmentation result are also discussed.In addition,we compare our algorithm with other image segmentation algorithms and discuss the advantages and disadvantages of our algorithm.